your problem was
x-7=14+x... so you would get the x values to one side, by subtracting or adding, then you would add 7 over because it was originally a negative... finally when you add those two together you get 21x, because the x was to the right of the 14 originally
x-7=14+x
-7=14x
21x

No bro, lines extend infinitely and if they are parallel, they never intersect. There's no such thing as lines connecting at infinity. The only way you can say that is if you've been to infinity. No one has, so no one can make such a claim.